Minimal Dynamical Triangulations of Random Surfaces

TL;DR

This paper introduces a simplified class of dynamical triangulations for 2D gravity, maintaining fractal properties and critical behavior of coupled Ising models, thus offering a minimal yet effective approach to quantum gravity simulations.

Contribution

It proposes a minimal set of local constraints in dynamical triangulations that preserves key geometric and physical properties of 2D quantum gravity models.

Findings

Fractal structure remains intact under vertex degree restrictions.

The Ising model exhibits a continuous phase transition with KPZ exponents.

Critical behavior is consistent with standard 2D gravity coupled models.

Abstract

We introduce and investigate numerically a minimal class of dynamical triangulations of two-dimensional gravity on the sphere in which only vertices of order five, six or seven are permitted. We show firstly that this restriction of the local coordination number, or equivalently intrinsic scalar curvature, leaves intact the fractal structure characteristic of generic dynamically triangulated random surfaces. Furthermore the Ising model coupled to minimal two-dimensional gravity still possesses a continuous phase transition. The critical exponents of this transition correspond to the usual KPZ exponents associated with coupling a central charge c=1/2 model to two-dimensional gravity.